I looked into it again, and it looks like this strategy works if in the opening card selection you get:
1) A total of 2 non-consumable healing
2) Some sort of scaling
After starting the first fight, sell two cards so you have 10 cards in your deck. Each 2 rounds, you will take 6 damage, and gain 4 life from basic heals and 2 life from your cards you picked up, keeping you at the same life total over time.
Some sort of enemy scaling might be the best way to fix this, because removing all types of scaling in the game would probably remove half of the effects :)